Checking date: 18/05/2022

Course: 2022/2023

Calculus II
Study: Bachelor in Biomedical Engineering (257)

Coordinating teacher: DEAÑO CABRERA, ALFREDO

Department assigned to the subject: Mathematics Department

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

Requirements (Subjects that are assumed to be known)
Calculus I, Linear Algebra
The student will be able to formulate, solve and understand mathematically the problems arising in Biomedical Engineering. To do so it is necessary to be familiar with the n-dimensional Euclidean space, making a special emphasis in dimensions 2 and 3, visualizing the more important subsets. He/she must be able to manage (scalar and vector) functions of several variables, as well as their continuity, differentiability, and integrability properties. The student must solve optimization problems with and without restrictions and will apply the main theorems of integration of scalar and vector functions to compute, in particular, lengths, areas and volumes, moments of inertia, and heat flow.
Skills and learning outcomes
Description of contents: programme
1. Differential Calculus in several variables 1.1. R^n as an Euclidean space; topology 1.2. Scalar and vector functions of n variables 1.3. Limits and continuity 1.4. Differentiability 2. Local properties of functions 2.1. Higher-order derivatives 2.1.1 Iterated derivatives 2.1.2. Differential operators: divergence, curl, laplacian 2.1.3. Taylor polynomial 2.2. Free and constrained optimization 2.2.1 Local extrema 2.2.2. Global extrema: free optimization problems 2.2.3. Lagrange multipliers 3. Integral Calculus in R^2 and R^3 3.1. Double and triple integrals 3.2. Changes of variables 3.3. Applications 4. Integrals over curves and surfaces 4.1. Line and path integrals 4.2. Surface integrals 4.3. Integral theorems of vector analysis
Learning activities and methodology
The learning methodology will include: - Attendance to master classes, in which core knowledge will be presented that the students must acquire. The recommended bibliography will facilitate the students' work - Resolution of exercises by the student that will serve as a self-evaluation method and to acquire the necessary skills - Exercise classes, in which problems proposed to the students are discussed - Tests - Final Exam - Tutorial sessions - The instructors may propose additional homework and activities
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Calendar of Continuous assessment
Basic Bibliography
  • J. E. Marsden and A. J. Tromba. Vector Calculus, 6th. edition. W. H. Freeman. 2012
  • M. D. Weir, J. Hass, and G. B. Thomas. Thomas¿ Calculus, Multivariable. Addison-Wesley. 2010
Additional Bibliography
  • J. Stewart. Calculus. Cengage. 2008
  • M. Besada, F. J. García, M. A. Mirás, and C. Vázquez. Cálculo de varias variables. Cuestiones y ejercicios resueltos. Garceta. 2011
  • M. J. Strauss, G. L. Bradley, and K. J. Smith. Multivariable Calculus. Prentice Hall. 2002
  • P. Pedregal Tercero. Cálculo Vectorial, un enfoque práctico. Septem Ediciones. 2001
  • R. Larson and B. H. Edwards. Calculus II, 9th. edition. Cengage. 2009
  • S. Salas, E. Hille, and G. Etgen. Calculus. One and several variables. Wiley. 2007
  • T. M. Apostol. Calculus. Wiley. 1975

The course syllabus may change due academic events or other reasons.